主动降噪技术详解：信号处理与应用实战

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"Active Noise Control (ANC): A Tutorial Review" 是一篇深入探讨有源噪声控制技术的论文。作者沈国（SENM.KUO）和邓恩·M·摩根（Dennis N. Morgan, IEEE Senior Member）在文中聚焦于实际应用中的主动降噪系统，尤其是针对信号处理算法的实践性和数字信号处理（DSP）在真实世界场景中的实现。该论文首先介绍了有源噪声控制的基本原理，即通过一系列辅助声源引入相位相反的“反噪声”波，来抵消环境噪声。这些辅助声源通过电子系统连接，并采用特定的信号处理算法来定制噪音消除策略。有源噪声控制的应用范围广泛，包括制造业、工业操作以及消费电子产品等领域。论文的核心内容是开发并分析单通道宽带前馈控制的基础自适应算法。这个算法随后被扩展到窄带前馈和自适应反馈控制，以应对不同频率范围的噪声。对于多通道情况，作者详细探讨了在线次级路径建模技术，如格子方法、频域方法、子带方法以及递归算法等，这些技术有助于提高系统的性能和鲁棒性。作者特别强调了实际应用中的挑战，如实时性、准确性以及抗干扰能力，这些都是设计有效ANC系统时必须考虑的关键因素。此外，论文还可能涉及误差分析、系统优化、算法稳定性和计算效率等问题，以及如何在有限的硬件资源下实现高效的主动降噪。 “Active Noise Control: A Tutorial Review”是一篇实用教程，旨在为读者提供从理论到实践的全面指导，帮助理解和掌握有源噪声控制技术在现代生活中的实际应用。通过阅读这篇论文，读者能够深入了解主动降噪系统的各个方面，包括信号处理策略、技术选择以及解决实际问题的策略。

Fig. 6. Block diagram of ANC system with feedback.

Fig. 7. ANC with acoustic feedback neutralization.

1) Feedback Neutralization: The simplest approach to

solving the feedback problem is to use a separate feedback

cancellation, or “neutralization,” ﬁlter within the controller,

which is exactly the same technique as used in acoustic echo

cancellation [43]. This electrical model of the feedback

path is driven by the secondary signal, and its output

is subtracted from the reference sensor signal [44]. A

duct-acoustic ANC system using the FXLMS algorithm

with feedback neutralization is illustrated in Fig. 7. The

feedback component of the reference microphone signal

is canceled electronically using a feedback neutralization

ﬁlter

which models the feedback path

Since the primary noise is highly correlated with the

antinoise, the adaptation of the feedback neutralization ﬁlter

must be inhibited when the ANC system is in operation,

similar to adaptive echo cancellation during periods of

double talk. Thus, feedback neutralization is achieved, in

effect, by using an ofﬂine adaptive method for determining

the transfer function of the feedback path. The models

and can be estimated simultaneously by using the

ofﬂine modeling technique [4].

2) Adaptive IIR Filter: Equation (14) shows that when

feedback is present, the optimal solution of the adaptive

ﬁlter is generally an IIR function with poles and zeros. This

rational function can be approximated by an FIR function

of sufﬁcient order, but a smaller step size

then has to

be used for stability reasons. The poles of an IIR ﬁlter

make it possible to obtain well-matched characteristics with

a lower order structure, thus requiring fewer arithmetic

Fig. 8. ANC system using the ﬁltered-U recursive LMS algo-

rithm.

operations [41]. However, the disadvantages of adaptive

IIR ﬁlters are: 1) IIR ﬁlters are not unconditionally stable

because of the possibility that some pole(s) of the ﬁlter

will move outside of the unit circle during the adaptive

process, causing instability; 2) the adaptation may converge

to a local minimum because the MSE function of adaptive

IIR ﬁlters is generally nonquadratic; and 3) IIR adaptive

algorithms can have a relatively slow convergence rate

in comparison with that of FIR ﬁlters. A comprehensive

discussion of adaptive IIR ﬁlters can be found in the

literature [45], [46].

A block diagram of an adaptive IIR ANC system [47]

is illustrated in Fig. 8. The output signal of the IIR ﬁlter

is computed as

(16)

where

is the weight

vector of

is the reference signal vector,

is the weight vector of and

is the output signal vector delayed by one sample.

Many algorithms can be employed to ﬁnd the optimal set

of coefﬁcients

and to minimize the error signal

In 1976, Feintuch [48] suggested that the recursion based

on the old output gradients is negligible. Based on this

suggestion, the “ﬁltered-U recursive LMS algorithm” [49]

for ANC is derived as [4]

(17)

(18)

where

is the ﬁltered version

of the canceling signal vector at time

In practice, it

is reasonable to use a higher order for

than for

[50]. Real-time experiments have been conducted to test

the system performance for various reference microphone

locations, error microphone locations, and different time-

varying sources, such as a centrifugal fan and diesel engine

[51].

Given the complexities associated with the pole-zero

structure of

and one cannot predict the

values to which

and will converge. Also, global

convergence and stability of the ﬁltered-U recursive LMS

948 PROCEEDINGS OF THE IEEE, VOL. 87, NO. 6, JUNE 1999

Authorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on August 6, 2009 at 09:24 from IEEE Xplore. Restrictions apply.

Fig. 9. Basic conﬁguration of narrow-band ANC system.

algorithm have never been proven formally. A modiﬁed

leaky version of the simpliﬁed hyperstable adaptive re-

cursive ﬁlter (SHARF) algorithm [52] has been developed

for ANC applications to improve the stability of the IIR

adaptive ﬁlter [53]. In that algorithm, a lowpass ﬁlter is

used to smooth the error signal for the ﬁltered-U recursive

LMS algorithm, thereby providing a higher stability margin.

III. N

ARROWBAND FEEDFORWARD ANC

Many noises are periodic, such as those generated by

engines, compressors, motors, fans, and propellers. Direct

observation of the mechanical motion of such sources

generally is possible by using an appropriate sensor, which

provides an electrical reference signal that contains the

fundamental frequency and all the harmonics of the primary

noise. However, this technique is only effective for periodic

noise because the fundamental driving frequency is the only

reference information available.

A. Introduction

A basic block diagram of narrow-band ANC for reducing

periodic acoustic noise in a duct is illustrated in Fig. 9. This

system controls harmonic sources by adaptively ﬁltering a

synthesized reference signal

internally generated by

the ANC system. This technique has the following advan-

tages: 1) undesired acoustic feedback from the canceling

loudspeaker back to the reference microphone is avoided;

2) nonlinearities and aging problems associated with the

reference microphone are avoided; 3) the periodicity of the

noise removes the causality constraint; 4) the use of an

internally generated reference signal results in the ability

to control each harmonic independently; and 5) it is only

necessary to model the acoustic plant transfer function over

frequencies in the vicinity of the harmonic tones; thus, an

FIR ﬁlter with substantially lower order may be used.

The reference signal generator is triggered by a syn-

chronization pulse from a nonacoustic sensor, such as a

tachometer signal from an automotive engine. In general,

two types of reference signals are commonly used in

narrow-band ANC systems: 1) an impulse train with a

period equal to the inverse of the fundamental frequency

of the periodic noise [54] and 2) sinewaves that have the

same frequencies as the corresponding harmonic tones to

be canceled. The ﬁrst technique is called the waveform

synthesis method, which was proposed by Chaplin [55].

The second technique embodies the adaptive notch ﬁlter,

which was originally developed for the cancellation of tonal

interference [56] and applied to periodic ANC [57].

The waveform synthesis method discussed next in

Section III-B employs synchronous sampling. However,

for some applications, the actual period will vary from

the nominal value as a function of loading conditions.

Therefore, it is sometimes desirable to operate asynchro-

nously with a ﬁxed sampling rate so that the secondary-path

estimate ﬁlter coefﬁcients do not have to be changed as

a function of actual machine rotation rate. Also, some

digital signal processors cannot be efﬁciently utilized on

a synchronous signal-driven basis. Asynchronous ANC

systems using the FXLMS algorithm eliminate the problem

of having to change

as the sampling rate varies and

are implicit in the later formulations of Sections III-C and

III-D.

B. Waveform Synthesis Method

1) Structures and Algorithms: The waveform synthesizer

[55] stores canceling noise waveform samples

in unique contiguous memory addresses,

where

is the number of samples over one cycle of the

waveform and

is the current time index. These samples

represent the required waveform to be generated and are

sequentially sent to a D/A converter to produce the actual

canceling noise waveform for the secondary loudspeaker.

Thus

(19)

represents the

th element of waveform samples, where

mod and can be implemented as a pointer

incremented in a circular fashion between zero and

for each sampling period, controlled by interrupts generated

from the synchronization signal.

The residual noise picked up by the error microphone

is synchronously sampled with the reference signal timing

pulses. In a practical system, there is a delay between the

time the signal

is fed to the loudspeaker

and the time it is received at the error microphone. This

delay can be accommodated by subtracting a time offset

from the circular pointer

Thus, the adaptation unit

adjusts the values of the waveform samples using a variant

of the LMS algorithm

otherwise

(20)

where

and is the time delay, which is

constant for a given loudspeaker-microphone arrangement,

is the sampling period, and greatest integer less

than or equal to

This offset number must be updated

as the sampling rate varies, since it is synchronized with

the noise source.

KUO AND MORGAN: ACTIVE NOISE CONTROL 949

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